f (x) = cos(x)Problem 2. Consider . Using thef(given function at X0 = 0by making use of the first 10 terms of the Taylor6approximateSeries expansion of J (). Solve the truncationerror.

Answered: Image /qna-images/answer/c402dfd1-6cd0-4ff1-a7a5-4bcf08a33872.jpg

Answered: Problem 2. Consider J (x) = Cos(x).…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4
You are given the position, velocity and acceleration of a particle at time t = 0. The position is p(0) = 2, the velocity v(0) = 4, and the acceleration a(0) = 3. Using this information, which Taylor series should they use to approximate p(t), and what is the estimated value of p(4) using this approximation?
#2. Find a power series representation (centered at a = 0) for the function below f(x) = = 1 1+x5 #3. Evaluate the indefinite integral using the series you found in problem #2. 1 1+x5 S dx
1. Sketch the graphs of the following series on the interval x E [-3L,3L], and give a brief explanation of the differences between them: (a) The Fourier Series of the function f (x) = et calculated using the interval (-L, L). (b) The Fourier Sine Series of f(x) = e" calculated using the interval (0, L). (c) The Fourier Cosine Series of f(x) = e" calculated using the interval (0, L).
6. Find the sine series of х, f(x) = 0
Q 3. Find the Taylor series of f at the point c for : (c) f(x) = sin x, c= T (d) f(x) = cos x, c = 5 (a) f(x) = e", c= 2 (b) f(x) = }, c = 1
Explain elaborately..
11
Problem 2. Consider (x) = cos(x). Using the s (#) 6. given function at by making use of the first 10 terms of the Taylor approximate Series expansion of J (). Solve the truncation f error.
Given cos(x) = (-1)" n=0 (2n)! -x2n for all x ER, Express the integral cos x dx as a power series.
f (x) = In (1+ x). Problem 3. Consider Using 0, f (3) the given function at To by making use of the first 9 terms of the Taylor approximate Series expansion of J (). Solve the truncation error.

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Problem 2. Consider J (x) = Cos(x). Using the given function at X0 = 0 by making use of the first 10 terms of the Taylor approximate Series expansion of J (x) s Solve the truncation error.